Method for observing a sample

ABSTRACT

A method for observing a sample includes illuminating the sample with a light source and forming a plurality of images, by an imager, the images representing the light transmitted by the sample in different spectral bands. From each image, a complex amplitude representative of the light wave transmitted by the sample is determined in a determined spectral band. The method further includes backpropagation of each complex amplitude in a plane passing through the sample, determining a weighting function from the back-propagated complex amplitudes, propagating the weighting function in a plane along which the matrix photodetector extends, updating each complex amplitude, in the plane of the sample, according to the weighting function propagated.

TECHNICAL FIELD

The technical field of the invention is related to the observation of asample, in particular a biological sample, by lensless imaging,implementing a holographic reconstruction algorithm with improvedperformance.

PRIOR ART

The observation of samples, and in particular biological samples, bylensless imaging has seen substantial growth over the last 10 years.This technique allows a sample placed between a light source and amatrix-array photodetector to be observed without the need to place anymagnifying optical lenses between the sample and the photodetector.Thus, the photodetector collects an image of the light wave transmittedby the sample.

This image is formed of interference patterns formed by interferencebetween the light wave emitted by the source and transmitted by thesample, and diffracted waves resulting from the diffraction, by thesample, of the light wave emitted by the source. These interferencepatterns are sometimes referred to as diffraction patterns.

Document WO2008090330 describes a device allowing biological samples, infact cells, to be observed by lensless imaging. The device allows aninterference pattern to be associated with each cell, the morphology ofthe interference pattern allowing the type of cell to be identified.Lensless imaging would thus appear to be a simple and inexpensivealternative to conventional microscopy. In addition, its field ofobservation is clearly larger that of a microscope can be. Thus it willbe understood that the potential avenues of application associated withthis technology are many. This document also mentions that it ispossible to illuminate the sample using light sources of variouswavelengths.

Document US2012/0218379, published after the preceding document, echoesmost of the teachings of WO2008090330, while also mentioning thepossible use of a color matrix-array photodetector; however, the colorinformation is subsequently processed to form a monochromatic image.

Generally, the image formed on the matrix-array photodetector, includingthe interference patterns, may be processed with a digital propagationalgorithm, so as to estimate optical properties of the sample. Suchalgorithms are well known in the field of holographic reconstruction. Todo this, the distance between the sample and the photodetector beingknown, a propagation algorithm taking into account this distance, andthe wavelength, is applied. It is then possible to reconstruct an imageof an optical property of the sample. A digital reconstruction algorithmis for example described in US2012/0218379.

It is also known that such algorithms may generate an image affected bya source of substantial background noise, referred to as the “twinimage”. Such noise is due to the fact that the initial image, formed bythe photodetector, contains only partial information on the light wavecollected by the photodetector. Specifically, an image providesinformation only on the real part of the light wave, this informationbeing obtained from the measured intensity. However such an imagecontains no information on the imaginary part of the light wave to whichthe detector is exposed, in particular its phase. The reconstructionalgorithm therefore uses incomplete information, this resulting in theappearance of noise in the reconstructed image.

Such background noise may complicate the interpretation of imagesreconstructed by digital propagation; it is important to decrease theinfluence thereof via suitable algorithms.

To do this, the publication “Lensless phase contrast microscopy based onmultiwavelenth Fresnel diffraction”, Optics Letters Vol. 39, No. 2, 15Jan. 2014, describes an algorithm allowing the quality of reconstructedimages to be improved. This publication describes a lensless imagingdevice based on the use of three light sources of different wavelengths(685 nm, 785 nm and 940 nm, respectively). The sample is illuminated insuccession by these three light sources. The photodetector then acquiresas many images as there are light sources, these images being formed ina plane, called the detector plane, in which the sensor lies. To eachimage corresponds one wavelength.

A first image, of a first wavelength, is back propagated, depending onsaid first wavelength, to a plane in which the object lies, called theobject plane, so as to obtain, in this object plane, a complex firstfield. The phase of this complex first field, in the object plane, ismultiplied by a ratio between the first wavelength and a secondwavelength. This complex field is then propagated, depending on saidsecond wavelength, from the object plane to the detector plane,subsequent to which its modulus is replaced by the modulus of the imageacquired at said second wavelength. It is then back propagated to theobject plane, for a second iteration. The iterative method continuesuntil a convergence criterion has been reached. Document WO2014035238,certain of the inventors of which are the authors of the aforementionedpublication, contains the same teachings.

The publication Bao P. “Optical surface profile measurement using phaseretrieval by, tuning the illumination wavelength”, Optics Communications285, 5029-5036, 2012 describes an iterative algorithm allowing athree-dimensional surface of a transparent object to be reconstructed onthe basis of an image acquired by an image sensor in a lenslessconfiguration. This algorithm aims to illuminate an object using twowavelengths. The image acquired by the image sensor, at each wavelength,is propagated to an object plane. A phase difference is then estimated,at each of these wavelengths, in the object plane. The three-dimensionalsurface is reconstructed on the basis of the phase difference thusestimated.

Document WO2015/015023 describes an iterative holographic reconstructionalgorithm based on a color image sensor in a lensless configuration.According to this algorithm, the sample is illuminated with apolychromatic light source. The acquired image is decomposed intovarious spectral components. Each component is back propagated to aplane in which the sample lies, the propagation of the components beingcarried out over distances that are different from one another. Thisdocument then describes mixing spectra of each hologram in the Fourierdomain, this allowing a single image to be generated, the latter beingused in a subsequent iterative loop.

The inventors provide an alternative method to those provided in thepreceding publications, allowing optical properties of a sample to bereliably estimated.

SUMMARY OF THE INVENTION

A first subject of the invention is a method for observing a sample,including the following steps:

-   -   i) illuminating said sample using a light source that is able to        produce a light wave that propagates along a propagation axis;    -   ii) acquiring, using a photodetector, a plurality of images of        the sample, said images being formed in a detection plane, the        sample being placed between the light source and the        photodetector, each image being representative of a light wave,        transmitted by the sample, under the effect of said        illumination, each image being acquired in a spectral band that        is different from the others;        the method being characterized in that it also comprises the        following steps:    -   iii) determining, on the basis of each image acquired in a        spectral band, an initial complex amplitude of the transmitted        light wave, in said spectral band, in said detection plane;    -   iv) back propagating each complex amplitude established in the        detection plane, in a spectral band, in order to determine a        complex amplitude of the transmitted wave, in each spectral        band, in a plane in which the sample lies;    -   v) combining a plurality of complex amplitudes determined in        step iv), in various spectral bands, in order to calculate a        weighting function in the sample plane;    -   vi) projecting said weighting function onto the detection plane        so as to obtain, for each spectral band, a weighting function in        said detection plane;    -   vii) updating each complex amplitude of the transmitted light        wave, in each spectral band, in the detection plane, using said        weighting function determined, in said spectral band, in step        vi);    -   viii) repeating steps iv to vii until a stop criterion is        reached.

Thus, each iteration comprises propagating, in an operation referred toas back propagation, from the detector plane to the sample plane, aplurality of complex amplitudes, in various spectral bands. Thesevarious complex amplitudes are combined, in the sample plane, to form aweighting function. This combination, in the sample plane, of aplurality of complex amplitudes, corresponding to various spectralranges, has the effect of smoothing the noise affecting each thereof,this noise being the consequence of the back propagation.

The weighting function is then propagated from the sample plane to thedetection plane, where it is used to form a new estimation of thecomplex amplitude of the light wave to which the sample is exposed, ineach spectral band in question.

Alternatively to the methods described in the prior art, the weightingfunction, in said sample plane, may be calculated by calculating aweighted sum of various complex amplitudes, or of their logarithms, inthe sample plane, of the transmitted light wave, said complex amplitudesrespectively being associated with various spectral bands. The weightingfunction, in said sample plane, may also be determined by calculating aweighted sum of the modulus and/or argument of various complexamplitudes, in the sample plane, of the transmitted light wave, saidcomplex amplitudes respectively being associated with various spectralbands.

By transmitted light wave, what is meant is the light wave to which thephotodetector is exposed.

The method may comprise any one of the following features alone or inany technically possible combination:

-   -   In step iii), the modulus of the complex amplitude of the        transmitted wave transmitted in a spectral band is determined by        normalizing the intensity of the image measured by the        photodetector 16, in said spectral band, by a reference        intensity measured by said photodetector in the absence of        sample.    -   In step iv), the complex amplitude in a sample plane, in a        spectral band, is determined by applying a propagation-axis        propagation operator to said complex amplitude defined in the        same spectral band in the detection plane.    -   In step vi), said weighting function, in the detection plane, is        obtained by applying a propagation-axis propagation operator to        the weighting function determined, in the sample plane, in step        v).    -   In step vii), the modulus of the complex amplitude of the        transmitted light wave, in a spectral band, in the detection        plane, is calculated depending on the modulus of said initial        complex amplitude, in said spectral band.    -   In step vii), the argument of the complex amplitude of the        transmitted light wave, in a spectral band, in the detection        plane, is calculated depending on the argument of the weighting        function determined, in said detection plane and in said        spectral band, in step vi).

In step v), said weighting function may be common to all the spectralbands. Alternatively, this step v) may comprise determining a pluralityof weighting functions, each weighting function being associated withone spectral band.

The method may include, following step viii), the step ix) of forming animage representative of the modulus or of the argument of the complexamplitude of the wave transmitted by the sample, in the sample plane orin the detection plane, in at least one spectral band (λ_(i)).

Another subject of the invention is a device for observing a sampleincluding:

-   -   a light source that is suitable for illuminating said sample;    -   a photodetector, the sample being placed between the light        source and the photodetector,    -   the photodetector being suitable for forming a plurality of        images, in a detection plane, of a light wave transmitted by the        sample under the effect of illumination by said light source,        each image being obtained in a spectral band that is different        from the others; and    -   a processor that is suitable for processing said plurality of        images by executing instructions, programmed into a memory,        implementing a method such as described above.

FIGURES

FIG. 1 shows a first example of a device for implementing the invention,the analyzed sample being an anatomopathology slide.

FIG. 2 shows a first example of a device for implementing the invention,the analyzed sample being a bodily liquid containing particles.

FIG. 3 shows the detection plane, on which an image is formed, and thesample plane. This figure also illustrates the relationships between themain quantities implemented in the various described embodiments.

FIG. 4 shows a flowchart illustrating the sequence of the main steps ofan iterative reconstructing method.

FIG. 5 shows a second example of a device for implementing theinvention, the analyzed sample being an anatomopathology slide.

FIGS. 6A, 6B and 6C show reconstructed images, in a sample plane, in afirst spectral band, reconstructed using an iterative reconstructionalgorithm, these images respectively being obtained following a numberof iterations respectively equal to 1, 3 and 10.

FIGS. 7A, 7B and 7C show reconstructed images, in a sample plane, in asecond spectral band, reconstructed using an iterative reconstructionalgorithm, these images respectively being obtained following a numberof iterations respectively equal to 1, 3 and 10.

FIGS. 8A, 8B and 8C show reconstructed images, in a sample plane, in athird spectral band, reconstructed using an iterative reconstructionalgorithm, these images respectively being obtained following a numberof iterations respectively equal to 1, 3 and 10.

FIGS. 9A, 9B and 9C show composite images obtained by combiningreconstructed images in the first, second and third spectral bands,these images respectively corresponding to 1, 3 and 10 iterations. Theseimages are color images, here shown in black and white.

SUMMARY OF PARTICULAR EMBODIMENTS

FIG. 1 shows an example of a device falling within the scope of theinvention. A light source 11 is able to emit a light wave 12, called theincident light wave, in the direction of a sample 10, along apropagation axis Z.

The sample 10 may be a biological sample that it is desired tocharacterize. It may for example be a tissue slide, or ananatomopathology slide, including a small thickness of tissue depositedon a transparent slide 15. By small thickness, what is meant is athickness preferably smaller than 100 μm, and preferably smaller than 10μm, typically a few microns. Such a sample is shown in FIG. 1. It may beseen that the sample lies in a plane P₀, called the sample plane,perpendicular to the propagation axis Z.

The sample 10 may also include a solid or liquid medium 14 containingparticles 1, 2, 3, 4, 5 to be characterized, such a case being shown inFIG. 2. It may for example be a question of biological particles in aculture medium, or in a bodily liquid. By biological particle, what ismeant is a cell, a bacterium or another microorganism, a mushroom, aspore, etc. The term particles may also designate microbeads, forexample metal microbeads, glass microbeads or organic microbeads, whichare commonly implemented in biological protocols. It may also be aquestion of insoluble droplets submerged in a liquid medium, for examplelipid droplets in an oil-in-water type emulsion. Thus, the term particledesignates both endogenous particles, initially present in the examinedsample, and exogenous particles, added to this sample before analysis.

Generally, a particle has a size advantageously smaller than 1 mm, oreven smaller than 500 μm, and preferably a size comprised between 0.5 μmand 500 μm.

The distance Δ between the light source and the sample is preferablylarger than 1 cm. It is preferably comprised between 2 and 30 cm.Preferably, the light source, seen by the sample, may be considered tobe a point source. This means that its diameter (or its diagonal) ispreferably smaller than one tenth and better still one hundredth of thedistance between the sample and the light source. Thus, preferably, thelight reaches the sample in the form of plane waves, or waves that maybe considered as such.

The light source 11 is able to produce a plurality of incident lightwaves 12 ₁ . . . 12 _(n), each i^(th) light wave 12 _(i) lying in ani^(th) spectral band λ_(i). The spectral bands 12 ₁ . . . 12 _(n) aredifferent from one another, and, preferably, do not overlap.

In the example device shown in FIGS. 1 and 2, the light source includesthree elementary light sources, namely three light-emitting diodes(LEDs) 11 ₁, 11 ₂ and 11 ₃ emitting in the spectral bands λ₁=450 nm-465nm; λ₂=520 nm-535 nm; A₃=620 nm-630 nm, respectively. Preferably, thereis no overlap between the various spectral bands; a negligible overlap,for example concerning less than 25% and better still less than 10% ofthe light intensity emitted, is however envisionable. In this example,the light source 11 includes a Cree (registered trademark) XLamp(registered trademark) MC-E multi-LED diode. This diode includes fourindividually addressable elementary light-emitting diodes, only three ofwhich are implemented in the context of this invention, the fourth beinga white LED. The elementary light sources may be temporally coherentsources, such as laser diodes. Other configurations of light sources 11are possible and described below.

The light source 11 is preferably a point source. It may in particularcomprise a diaphragm 18, or spatial filter. The aperture of thediaphragm is typically comprised between 5 μm and 1 mm, preferablybetween 50 μm and 500 μm, and is for example 150 μm. The diaphragm maybe replaced by an optical fiber, a first end of which is placed facingone elementary light source 11 ₁, 11 ₂ or 11 ₃, and a second end ofwhich is placed facing the sample.

The light source 11 preferably includes a diffuser 17, placed betweeneach elementary light source 11 ₁, 11 ₂ and 11 ₃ and the diaphragm 18.The inventors have observed that the use of such a diffuser allowsconstraints on the centrality of each elementary light source withrespect to the aperture of the diaphragm to be relaxed. In other words,the use of such a diffuser allows an elementary light source 11 i, with1≤i≤3, that is slightly off center with respect to the aperture of thediaphragm 18 to be used. In this example, the diaphragm is sold byThorlabs under the reference P150S.

Preferably, each elementary light source 11 _(i) is of small spectralwidth, for example smaller than 100 nm, or even than 20 nm. The termspectral width designates the full width at half maximum of the emissionband of the light source in question.

In this example, the diffuser implemented is a 40° diffuser (referenceLight Shaping Diffuser 40°, manufactured by Luminit). The function ofsuch a diffuser is to distribute the light beam, produced by anelementary light source 11 _(i), over a cone of angle α, α being equalto 40° in the present case. Preferably, the scattering angle α variesbetween 10° and 60°.

The sample 10 is placed between the light source 11 and a matrix-arrayphotodetector 16. The latter preferably lies parallel, or substantiallyparallel to the transparent slide 15 holding the sample.

The term substantially parallel means that the two elements may not berigorously parallel, an angular tolerance of a few degrees, smaller than10° being acceptable.

The photodetector 16 is an imager, able to form an image in a detectionplane P. In the example shown, it is a CCD or CMOS matrix-arrayphotodetector including a pixel matrix-array. CMOS photodetectors arepreferred, because the size of the pixels is smaller, thereby allowingimages to be acquired the spatial resolution of which is more favorable.In this example, the detector is a CMOS sensor sold by Omnivision underthe reference OV5647. It is an RGB CMOS sensor comprising 2592×1944pixels, with an inter-pixel pitch of 1.4 μm. The useful area of thephotodetector is 3.6×2.7 mm². The detection plane P preferably liesperpendicular to the propagation axis Z of the incident light wave 12.

Preferably, the photodetector comprises a pixel matrix-array, abovewhich matrix array is placed a transparent protective window. Thedistance between the pixel matrix-array and the protective window isgenerally comprised between a few tens of μm to 150 or 200 μm.Photodetectors, the inter-pixel pitch of which is smaller than 3 μm, arepreferred, in order to improve the spatial resolution of the image. Thephotodetector may comprise a mirror-type system for redirecting imagestoward a pixel matrix-array, in which case the detection planecorresponds to the plane in which the image-redirecting system lies.Generally, the detection plane P corresponds to the plane in which animage is formed.

The distance d between the sample 10 and the pixel matrix-array of thephotodetector 16 is, in this example, equal to 300 μm. Generally,whatever the embodiment, the distance d between the sample and thepixels of the photodetector is preferentially comprised between 50 μmand 2 cm, and preferably comprised between 100 μm and 2 mm.

The absence of magnifying optics between the photodetector 16 and thesample 10 will be noted. This does not prevent focusing micro-lensesoptionally being present level with each pixel of the photodetector 16,these lenses not having the function of magnifying the image.

FIG. 3 shows a sample 10, including diffracting objects 32 placed aroundnon-diffracting or not very diffracting zones 31, which are qualifiedpoor zones below. The sample may be solid, for example in the case of atissue deposited on an anatomopathology slide. It may also be liquid,for example in the case of a bodily liquid or a cell culture medium.

The photodetector 16 is able to produce an image I_(i) of a light wave22 _(i) transmitted by the sample 10 when the latter is illuminated byan incident wave 12 _(i), in the i^(th) spectral band λ_(i). Thespectral band of the transmitted light wave 22 _(i) includes all or someof the spectral band of the incident wave 12 _(i). The light wave 22_(i), transmitted by the sample, in the spectral band λ_(i), resultsfrom the interaction of the sample 10 with the incident light wave 12_(i) produced by the elementary light source 11 _(i).

Under the effect of the incident light wave 12 _(i), the sample 10 maygenerate a diffracted wave that is liable to produce, level with thedetection plane P, interference, in particular with a portion of theincident light wave 12 _(i) transmitted by the sample. This interferencegives rise, in the image acquired by the photodetector, to a pluralityof elementary diffraction patterns, each elementary diffraction pattern36 including a central zone and a plurality of concentric diffractionrings. Each elementary diffraction pattern 36 is due to one diffractingobject 32 in the sample.

Moreover, the sample may absorb a portion of the incident light wave 12_(i). Thus, the light wave 22 _(i), in a spectral band λ_(i),transmitted by the sample, and to which the matrix-array photodetector16 is exposed, may comprise:

-   -   a component resulting from the diffraction, described above,        this diffraction component possibly in particular resulting in        the presence of elementary diffraction patterns on the        photodetector 16, each elementary diffraction pattern possibly        being associated with one diffracting element 32 of the sample.        Such a diffracting element may be a cell, or a particle, or any        other diffracting object 32 present in the sample 10.    -   a component resulting from the absorption of the incident light        wave 12 _(i) in the sample.

A processor 20, for example a microprocessor, is able to process eachimage generated by the matrix-array photodetector 16. In particular, theprocessor is a microprocessor connected to a programmable memory 23 inwhich a sequence of instructions for carrying out the calculating andimage-processing operations described in this description is stored. Itmay also be connected to a display screen 24.

The steps of an iterative method for obtaining an image of the sample 10will be described below with reference to FIGS. 3 and 4.

1^(st) Step: Initialization

In a first step 100 of acquiring images, each elementary light source 11_(i) of the light source 11 is activated in succession, each lightsource emitting an incident light wave (12 ₁, . . . 12 _(N)), in aspectral band (λ₁, . . . λ_(N)), along a propagation axis Z, in thedirection of the sample 10.

In each acquisition, the matrix-array photodetector captures an imageI_(i) corresponding to a spectral band λ_(i), the index i, relating tothe spectral band, being comprised between 1 and N, N being the numberof spectral bands in question. In the example shown in FIGS. 1 and 2,the light source 11 includes three elementary light sources 11 ₁, 11 ₂and 11 ₃. The photodetector captures three images I₁, I₂, I₃,corresponding to the spectral bands λ₁, λ₂ and λ₃, respectively.

The sample is placed at an axial coordinate z=0, along the propagationaxis Z. The letter r designates a radial coordinate, i.e. a coordinatein a plane perpendicular to the propagation axis Z. The plane z=dcorresponds to the detection plane, whereas the plane z=0 corresponds toa plane passing through the sample, called the sample plane and denotedP₀.

If I_(i) ^(z=d)(r)=I_(i) ^(d)(r) designates the value of the intensitycaptured, in the spectral band λ_(i), by the pixel of the detector ofradial coordinate r in the detection plane, it is possible to establish,using the image I_(i), a complex amplitude 60 _(i) ^(z=d)(r)=α_(i)^(d)(r) of the wave 22 _(i) at said pixel of coordinate r, the modulusof which may be expressed by the expression:|α_(i) ^(d)(r)|=√{square root over (I _(i) ^(d)(r))}

The exponent d expresses the fact that the complex amplitude isdetermined in the sample plane P, of equation z=d. The complex amplitudeα_(i) ^(d)(r) includes a modulus and an argument, such that:α_(i) ^(d)(r)=M _(i) ^(d)(r)e ^(jφ) ^(i) ^(d) ^((r))where:

-   -   M_(i) ^(d)(r) is the modulus of the complex amplitude of the        light wave detected by the photodetector, in the i^(th) spectral        band λ_(i), at a radial coordinate r in the detection plane; and    -   φ_(i) ^(d)(r) is the phase of the complex amplitude of the light        wave detected by the photodetector, in the i^(th) spectral band        λ_(i), and at said radial coordinate r in the detection plane.

However, the matrix-array photodetector delivers no information on thephase of the light wave. Thus, in step 100, e^(jφ) ^(i) ^(d) ^((r)) isconsidered to be equal to an arbitrary initial value, for example equalto 1.

The complex amplitude α_(i) ^(d)(r) may be expressed, normalized, by theexpression:

${A_{i}^{d}(r)} = \frac{\alpha_{i}^{d}(r)}{\sqrt{I_{i}^{mean}}}$where:

-   -   I_(i) ^(mean) is the mean intensity of the light wave 12 _(i)        emitted by the light source 11 in the i^(th) spectral band        λ_(i); this mean intensity may be determined experimentally, by        placing the photodetector 16 facing the light source 11, without        a sample placed therebetween, and by calculating the mean of the        pixels of the image acquired by the photodetector 16.    -   A_(i) ^(d)(r) is the normalized complex amplitude of the light        wave 22 _(i) detected by the matrix-array photodetector 16 in        the i^(th) spectral band λ_(i).

The normalization may also be carried out by dividing the complexamplitude α_(i) ^(d)(r) by I_(i) ^(mean)(r), this term representing thelight intensity, at the radial coordinate r, measured in the absence ofsample.

The normalized complex amplitude A_(i) ^(d)(r) includes a modulus and anargument, such that:A _(i) ^(d)(r)=m _(i) ^(d)(r)e ^(jφ) ^(i) ^(d) ^((r))where:

-   -   m_(i) ^(d)(r) is the modulus of the normalized complex amplitude        A_(i) ^(d)(r); and    -   φ_(i) ^(d)(r) is the phase of the normalized complex amplitude,        which is also the phase of the complex amplitude α_(i) ^(d)(r).

The first step 100 allows, on the basis of the image I_(i) detected bythe photodetector in the i^(th) spectral band λ_(i), an initial value tobe assigned to each complex amplitude α_(i) ^(d)(r) or to eachnormalized complex amplitude A_(i) ^(d)(r), such that:α_(i,p=1) ^(d)(r)=M _(i) ^(d)(r)=√{square root over (I _(i) ^(d)(r))}or

${A_{i,{p = 1}}^{d}(r)} = {{m_{i}^{d}(r)} = {\sqrt{\frac{I_{i}^{d}(r)}{I_{i}^{mean}}}.}}$

The index p corresponds to the rank of the iteration of the iterativemethod described below. Step 100 being an initialization step, the value1 is attributed to this index.

By addressing all or some of the pixels r of the photodetector 16, acomplex image, or complex field, of the light wave 22 _(i) in thedetector plane is obtained, this image containing the complex amplitudesα_(i) ^(d)(r) or the normalized complex amplitudes A_(i) ^(d)(r).

In the rest of the description, only the normalized complex amplitudeA_(i) ^(d)(r) will be considered, though the reasoning also applies tothe complex amplitude α_(i) ^(d)(r).

This first step is repeated for each spectral band (λ₁ . . . λ_(N))detected by the photodetector.

2^(nd) Step: Back Propagation to the Sample Plane P₀

During a second step 200, the normalized complex amplitude A_(i,p)^(d)(r) of the wave 22 _(i) to which the detector is exposed isestimated, in the sample plane P₀. This estimation is made by backpropagating the normalized complex amplitude A_(i,p) ^(d)(r), determinedin the detection plane P, from the detection plane P to the sample planeP₀.

The index p designates the rank of the iteration. In the first iteration(p=1), the initial normalized complex amplitude A_(i,p=1) ^(d)(r)=A_(i)^(d)(r) obtained at the end of the first step 100 is used. In thefollowing iterations (p>1), the complex amplitude resulting from thepreceding iteration is used, as will be detailed below.

According to well-known principles of digital holographicreconstruction, by determining the product of a convolution between thecomplex amplitude of the light wave 22 _(i) determined, for the spectralband λ_(i), in the detection plane z=d, and a propagation operatorh(r,z), it is possible to reconstruct a complex amplitude of the samelight wave at any point of spatial coordinates (r,z), and in particularin the sample plane P₀.

In other words, the normalized complex amplitude A_(i,p) ^(z)(r) of thelight wave 22 _(i) may be obtained, at a point of coordinates (r, z), onthe basis of A_(i,p) ^(z=d)(r), via the operation:A _(i,p) ^(z)(r)=A _(i,p) ^(z=d)(r)*h _(λi)(r,z−d),where h_(λi) is the propagation operator in the spectral band λ_(i).

When the reconstruction is carried out in the direction of propagationof the light, for example from the sample to the photodetector,propagation is spoken of. When the reconstruction is carried out in thedirection opposite the direction of propagation of the light, forexample from the photodetector to the sample, back propagation is spokenof.

The propagation operator may in particular be based on the Fresneldiffraction model. In this example, the propagation operator is theFresnel-Helmholtz function:

${h\left( {r,z} \right)} = {\frac{1}{j\;\lambda\; z}e^{j\; 2\pi\frac{z}{\lambda}}{\exp\left( {j\;\pi\frac{r^{2}}{\lambda\; z}} \right)}}$where λ is the wavelength.

Thus,

${A_{i,p}^{z = 0}(r)} = {{A_{i,p}^{0}(r)} = {{{A_{i,p}^{z = d}(r)}*{h_{\lambda\; i}\left( {r,{- d}} \right)}} = {{{- \frac{1}{j\;\lambda_{i}z}}e^{{- j}\; 2\pi\frac{z}{\lambda_{i}}}{\int{\int{{A_{i,p}^{d}\left( r^{\prime} \right)}\exp}}}} - {\left( {j\;\pi\frac{\left( {r - r^{\prime}} \right)^{2}}{\lambda_{i}d}} \right){dr}^{\prime}}}}}$where

-   -   r′ designates the radial coordinates in the plane of the        photodetector (z=d);    -   r designates the radial coordinates in the reconstruction plane        (z=0); and    -   λ_(i) is the central wavelength of the spectral band in        question.

A_(i,p) ⁰(r) is therefore obtained by back propagating A_(i,p) ^(d)(r)over the distance d separating the detection plane P from the sampleplane P₀.

This second step is repeated for each spectral band (λ₁ . . . λ_(N))emitted by the light source 11 or, more generally, for each spectralband (λ₁ . . . λ_(N)) respectively associated with each image (I₁ . . .I_(N)) detected by the photodetector 16.

It is possible, at this stage, to establish an image of the modulus orof the phase of the complex amplitude A_(i,p) ⁰(r) of each light wave 22_(i), in the sample plane P₀, whether the complex amplitude benormalized or not, by calculating the value of A_(i,p) ⁰(r) at thevarious coordinates r in the sample plane.

Each image of the modulus of the complex amplitude A_(i,p) ⁰(r) isrepresentative of the intensity of the light wave level with the sample,whereas each image of the argument of the complex amplitude A_(i,p) ⁰(r)is representative of the phase of the intensity of the light wave levelwith the sample.

When, as in the present case, three spectral bands centered respectivelyon wavelengths in the blue, green and red, are used, the informationcontained in the three images allows a color image of the sample to beobtained.

It will be noted that the normalized complex amplitude A_(i,p) ⁰(r) isequivalent to a transmission function describing transmission of theincident wave 12 _(i) by the sample 10 at the radial coordinate r.

3^(rd) Step: Determining the Weighting Function

In the step 300, a weighting function, denoted F_(p) ⁰(r), allowing thecomplex amplitude of the light wave transmitted by the sample in thevarious spectral bands λ_(i) in question to be weighted, is determined,in the sample plane.

According to this example, the weighting function F_(p) ⁰(r), in thesample plane, may be common to each spectral band. It is obtained bycombining the normalized complex amplitudes A_(i,p) ⁰(r) of the lightwave transmitted by the sample, in the sample plane P₀ and in thevarious spectral bands λ_(i).

According to one example, the weighting function is obtained via aweighted sum of each complex amplitude determined in step 200, in thesample plane P₀, using the expression:

${F_{p}^{0}(r)} = {\frac{1}{\sum\limits_{i}\; k_{i}}{\sum\limits_{i}\;{k_{i}{A_{i,p}^{0}(r)}}}}$where k_(i) is a positive weighting factor associated with the i^(th)spectral band λ_(i).

The weighting factors may be equal to one another, for example equal to⅓.

Other ways of determining the weighting function, in the sample plane,are detailed below.

4^(th) Step: Propagation of the Weighting Function to the Detector Plane

The step 400 aims to propagate, from the sample plane P₀ to the detectorplane P, the weighting function F_(p) ⁰(r) determined, in the precedingstep, in the sample plane P₀. Since the propagation operator isdependent on wavelength, this propagation is carried out for eachspectral band λ_(i) in question.

Thus, for each spectral band λ_(i), F_(i,p) ^(d)(r)=F_(p)⁰(r)*h_(λi)(r,z=d).

When the propagation operator is a Fresnel-Helmholtz operator such asdefined above,

${F_{i,p}^{d}(r)} = {\frac{1}{j\;\lambda_{i}d}e^{{- j}\; 2\pi\frac{d}{\lambda_{i}}}{\int{\int{{F_{i,p}^{0}\left( r^{\prime} \right)}{\exp\left( {j\;\pi\frac{\left( {r - r^{\prime}} \right)^{2}}{\lambda_{i}d}} \right)}{dr}^{\prime}}}}}$

Since the propagation operator is dependent on wavelength, as manyweighting functions are determined, in the detection plane, as there arespectral bands.

-   -   r′ designates the radial coordinates in the sample plane (z=0);    -   r designates the radial coordinates in the reconstruction plane,        i.e. in the detector plane (z=d); and    -   λ_(i) is the central wavelength of the spectral band in        question.        5^(th) Step: Update of the Complex Amplitude in the Detector        Plane

In the step 500, the value of the weighting function, in the detectionplane z=d, is used to update the estimation of the normalized complexamplitude A_(i,p) ^(d)(r) of the light wave 22 _(i) to which thephotodetector 16 is exposed in the spectral band λ_(i).

The updating formula is:

${A_{i,p}^{d}(r)} = {{{m_{i}^{d}(r)} \times \frac{F_{i,p}^{d}(r)}{{F_{i,p}^{d}(r)}}} = {{m_{i}^{d}(r)} \times e^{j{{\overset{\sim}{\varphi}}_{i,p}^{d}{(r)}}}}}$where:

-   -   |F_(i,p) ^(d)(r)| is the modulus of F_(i,p) ^(d)(r);    -   m_(i) ^(d)(r) is the modulus of the normalized initial complex        amplitude A_(i,p) ^(d)(r) determined, on the basis of the image        I_(i), in the first step 100. This term serves as a link to the        measured data;    -   {tilde over (φ)}_(i,p) ^(d) is an estimation of the phase of the        complex amplitude of the wave 22 _(i) in the i^(th) spectral        band λ_(i); and    -   A_(i,p) ^(d)(r) is the complex amplitude of the light wave 22        _(i) transmitted by the sample, in the plane of the        photodetector 16, this complex amplitude forming the base of the        following iteration.

Following this step, a new iteration may start, the input datum of thisnew iteration p+1 being A_(i,p+1) ^(d)(r)=A_(i,p) ^(d)(r), this newiteration starting with the back propagation of each normalized complexamplitude A_(i,p+1) ^(d)(r), for the various spectral bands in question,to the sample plane P₀, according to step 200.

Steps 200 to 500 are carried out iteratively, either to a preset numberof iterations p_(max) or until a convergence criterion is reached, thelatter possibly being, for example, expressed in the form of adiscrepancy between the estimation of two given quantities in twosuccessive iterations. When this discrepancy is smaller than a giventhreshold ε, the convergence criterion is reached. For example, theprocess is stopped when one of these conditions is reached:

${{{\frac{F_{i,p}^{d}(r)}{{F_{i,p}^{d}(r)}} - \frac{F_{i,{p + 1}}^{d}(r)}{{F_{i,{p + 1}}^{d}(r)}}}} < ɛ};$F_(i, p)⁰(r) − F_(i, p + 1)⁰(r) < ɛ;A_(i, p)⁰(r) − A_(i, p + 1)⁰(r) < ɛ;Arg(A_(i, p)⁰(r) − A_(i, p + 1)⁰(r)) < ɛ;this list is not limiting.

At the end of the method, an estimation of the complex amplitude of thelight wave 22 _(i), transmitted by the sample, and to which thephotodetector is exposed, in the detector plane P, of equation z=d,and/or in the sample plane P₀, of equation z=0, is obtained, for eachspectral band in question. Using the various complex amplitudes A_(i,p)⁰(r) reconstructed in the sample plane, a precise representation of thelatter is obtained, in each of the spectral bands in question, inparticular by forming images on the basis of the modulus or of the phaseof said complex amplitudes.

As previously mentioned, when the spectral bands are spread over thevisible spectrum, the modulus or phase images may be combined, forexample superposed, so as to obtain representations in color.

It will be recalled that this algorithm, although described in relationto a normalized complex amplitude A_(i), also applies to thenon-normalized complex amplitude α_(i).

Contribution of the Weighting Function

One of the important points of this iterative algorithm is theconstruction of the weighting function F⁰(r) in the sample plane.Specifically, generally, it is insufficient to determine the complexamplitude of a light wave on the basis of an image acquired by aphotodetector, because information as to the phase of the wave is notrecorded by the photodetector, the latter being sensitive only tointensity, which corresponds to the modulus of the complex amplitude ofthe wave.

Thus, as indicated in the description of step 100, the complex amplitudeα_(i) ^(d)(r) or normalized complex amplitude A_(i) ^(d)(r) determinedin this step contains no information as to the phase of the light wavethat they represent. This lack of information results, during the backpropagation from the detector plane P to the sample plane P₀, which isthe subject matter of step 200, in the formation of artefacts that arereferred to as twin images.

The inventors have observed that these artefacts mainly affect poorzones 31 located in the vicinity of diffracting elements 32, i.e., zoneslocated between two adjacent diffracting elements 32. Furthermore, theyhave observed that these artefacts are liable to fluctuate as a functionof wavelength. Thus, artefacts in the poor zones 31 may be averaged outstatistically by combining, for various wavelengths, the complexamplitudes back propagated to the sample plane. This statisticalsmoothing then increases the signal-to-noise ratio in the complex imageback propagated to the sample plane. Generally, the method amounts to:

-   -   obtaining an initial estimation A_(i,p=1) ^(d)(r) of the complex        amplitude of the wave 22 _(i) transmitted by the sample, in the        detector plane, and in a plurality of spectral bands (step 100);    -   back propagating each of these complex amplitudes to the sample        plane, in order to obtain, in each spectral band, a complex        amplitude A_(i,p) ⁰(r) in the sample plane (step 200);    -   calculating a weighting function F_(p) ⁰(r) weighting each        complex amplitude in the sample plane (step 300), so as to        decrease the influence of twin-image artefacts;    -   propagating said weighting function to the detector plane, for        at least one spectral band (step 400); and    -   updating the estimation of the complex amplitude A_(i,p) ^(d)(r)        of the wave 22 _(i) transmitted by the sample, in the detector        plane, and in a plurality of spectral bands, using the weighting        function F_(i,p) ^(d)(r) propagated to the detector plane (step        500).

The updating formula of step 500 shows that in each iteration, themodulus m_(i) ^(d)(r) (M_(i) ^(d)(r), respectively) of the normalizedcomplex amplitude A_(i,p) ^(d)(r) (of the complex amplitude α_(i)^(d)(r), respectively), in the detection plane, corresponds to thatdetermined, in step 100, with each image I_(i) formed by thephotodetector 16 in the spectral band λ_(i). In other words, in thevarious iterations, the modulus, in the detection plane, of the complexamplitude α_(i) ^(d)(r) or of the normalized complex amplitude A_(i,p)^(d)(r) does not vary and corresponds to that derived from the intensitymeasured by the photodetector.

In contrast, the algorithm tends to cause, in each update, a variationin the argument of the complex expression A_(i,p) ^(d)(r) or α_(i)^(d)(r), and in particular in the estimation of the phase {tilde over(φ)}_(i,p) ^(d), the latter being considered to be equal to the phase ofthe weighting function F_(i,p) ^(d)(r) propagated to the detector plane,at each wavelength λ_(i).

Thus, in this algorithm, each iteration comprises:

-   -   updating the complex amplitude A_(i,p) ^(d)(r) of each light        wave in the sample plane P₀ (step 200);    -   updating the argument of each complex amplitude A_(i,p) ^(d)(r),        and in particular its phase, in the detection plane (step 500).        Generation of the Weighting Function

A first way of calculating the weighting function consists in assigningan equal weight to the various spectral bands λ_(i) in question.

For example, the weighting function take the form

${{F_{p}^{0}(r)} = {\frac{1}{\sum\limits_{i}\; k_{i}}{\sum\limits_{i}\;{k_{i}{A_{i,p}^{0}(r)}}}}},$where k_(i) is the weighting factor, or weight, attributed to the i^(th)spectral band λ_(i), as described above with reference to step 300. Eachweighting factor k_(i) is positive and may have the same value, forexample ⅓.

According to one variant, and this applies in particular in the casewhere the sample analyzed is dyed, in a spectral range λ₀, the moduli ofthe complex amplitudes of first light waves 22 _(i) the spectral bandsλ_(i) of which are close to the spectral range λ₀ have a higher valuethan the moduli of the complex amplitudes of second light waves thespectral bands of which are further from the wavelength λ₀. In such acase, it is preferable to under-weight the complex amplitudes of thefirst light waves, and to over-weight the complex amplitudes of thesecond light waves.

For example, if the sample is dyed using a blue dye, which correspondsin our example to the first spectral band λ₁, the weighting factor k₁ islower than the weighting factors k₂ and k₃ associated with the spectralbands λ₂ (green) and λ₃ (red), respectively.

According to another variant, the modulus and the argument of eachcomplex amplitude are weighted by independent weighting factors, suchthat

${{F_{p}^{0}(r)}} = {\frac{1}{\sum\limits_{i}\; k_{i}}{\sum\limits_{i}\;{k_{i}{{A_{i,p}^{0}(r)}}}}}$${{Arg}\left( {F_{p}^{0}(r)} \right)} = {\frac{1}{\sum\limits_{i}\; k_{i}^{\prime}}{\sum\limits_{i}\;{k_{i}^{\prime}{{Arg}\left( {A_{i,p}^{0}(r)} \right)}}}}$k_(i) and k′_(i) being weighting factors respectively associated withthe modulus and the argument of the complex amplitude of the light wave22 _(i), in the sample plane, in the spectral band λ_(i).

According to another variant, the combination of the complex amplitudesA_(i,p) ⁰(r) takes the form of a sum of logarithms, according to theexpression:

${\ln\left( {F_{p}^{0}(r)} \right)} = {\frac{1}{\sum\limits_{i}\; k_{i}}{\sum\limits_{i}\;{k_{i}{\ln\left\lbrack {A_{i,p}^{0}(r)} \right\rbrack}}}}$

According to another variant, rather than one weighting function F_(p)⁰(r), a plurality of weighting functions F_(i,p) ⁰(r) are determined inthe sample plane, each function being associated with one spectral bandλ_(i).

Each weighting function F_(i,p) ⁰(r) associated with an i^(th)wavelength is obtained by combining a plurality of complex amplitudesA_(i,p) ⁰(r), respectively associated with various spectral bands.

In a first example, considering three spectral bands:

$\begin{bmatrix}F_{1,p}^{0} \\F_{2,p}^{0} \\F_{3,p}^{0}\end{bmatrix} = {\begin{bmatrix}k_{1,1} & k_{1,2} & k_{1,3} \\k_{2,1} & k_{2,2} & k_{2,3} \\k_{3,1} & k_{3,2} & k_{3,3}\end{bmatrix}\begin{bmatrix}{A_{1,p}^{0}(r)} \\{A_{2,p}^{0}(r)} \\{A_{3,p}^{0}(r)}\end{bmatrix}}$

Thus, according to this embodiment, the weighting function takes theform of a vector {right arrow over (F_(p) ⁰)}(r), of dimension N, Nbeing the number of spectral bands in question, each term F_(i,p) ⁰(r)of which is a weighting function associated with one spectral bandλ_(i). This weighting function may be obtained via the following matrixproduct:{right arrow over (F _(p) ⁰)}(r)=K{right arrow over (A _(p) ⁰)}

Where K is a weighting matrix, each term k_(i,j) of the weighting matrixrepresenting the weight associated with the complex amplitude A_(j,p)⁰(r) associated with the spectral band λ_(j) for the calculation of theweighting function associated with the spectral band λ_(i).

The matrix K is a square matrix of N by N size, N being the number ofspectral bands in question.

The weighting function is preferably normalized, such that each termF_(i,p) ⁰ may be expressed in the form:

${F_{i,p}^{0}(r)} = {\frac{1}{\sum\limits_{j}\; k_{i,j}}{\sum\limits_{j}\;{k_{i,j}{A_{j}^{0}(r)}}}}$the term

$\frac{1}{\sum\limits_{j}\; k_{i,j}}$being a normalization term.

According to a second example of this embodiment, again consideringthree spectral bands,

$\begin{bmatrix}{{F_{1,p}^{0}(r)}} \\{{F_{2,p}^{0}(r)}} \\{{F_{3,p}^{0}(r)}} \\{\arg\left( {F_{1,p}^{0}(r)} \right)} \\{\arg\left( {F_{2,p}^{0}(r)} \right)} \\{\arg\left( {F_{3,p}^{0}(r)} \right)}\end{bmatrix} = {{\begin{bmatrix}k_{1,1} & k_{1,2} & k_{1,3} & k_{1,4} & k_{1,5} & k_{1,6} \\k_{2,1} & k_{2,2} & k_{2,3} & k_{2,4} & k_{2,5} & k_{2,6} \\k_{3,1} & k_{3,2} & k_{3,3} & k_{3,4} & k_{3,5} & k_{3,6} \\k_{4,1} & k_{4,2} & k_{4,3} & k_{4,4} & k_{4,5} & k_{4,6} \\k_{5,1} & k_{5,2} & k_{5,3} & k_{5,4} & k_{5,5} & k_{5,6} \\k_{6,1} & k_{6,2} & k_{6,3} & k_{6,4} & k_{6,5} & k_{6,6}\end{bmatrix}\begin{bmatrix}{{A_{1,p}^{0}(r)}} \\{{A_{2,p}^{0}(r)}} \\{{A_{3,p}^{0}(r)}} \\{\arg\left( {A_{1,p}^{0}(r)} \right)} \\{\arg\left( {A_{2,p}^{0}(r)} \right)} \\{\arg\left( {A_{3,p}^{0}(r)} \right)}\end{bmatrix}}.}$

Thus, according to this embodiment, the weighting function takes theform of a vector {right arrow over (F_(p) ⁰)}(r), of dimension 2N, Nbeing the number of spectral bands in question, each term of which iseither the modulus or the argument of a weighting function F_(i,p) ⁰(r)associated with one spectral band λ_(i). This weighting function may beobtained via the following matrix product:{right arrow over (F _(p) ⁰)}(r)=K{right arrow over (A _(p) ⁰)}

Where K is a weighting matrix, of 2N×2N size, each term k_(i,j) of theweighting matrix representing the weight associated either with theargument or with the modulus of the complex amplitude A_(j,p) ⁰(r)associated with the spectral band λ_(j).

According to this embodiment, each coordinate of the vector {right arrowover (A_(p) ⁰)} represents either the modulus, or the argument, of acomplex amplitude A_(j,p) ⁰(r), in a spectral band j.

Just as in the preceding example, the weighting function is preferablynormalized, such that each term F_(i,p) ⁰ may be expressed in the form:

${{F_{i,p}^{0}(r)}} = {\frac{1}{\overset{3}{\sum\limits_{j = 1}}\; k_{i,j}}{\underset{j = 1}{\sum\limits^{3}}\;{k_{i,j}{{A_{j,p}^{0}(r)}}}}}$${{Arg}\left( {F_{i,p}^{0}(r)} \right)} = {\frac{1}{\overset{6}{\sum\limits_{j = 4}}\; k_{i,j}}{\overset{6}{\sum\limits_{j = 4}}\;{k_{i,j}{\arg\left( {A_{j,p}^{0}(r)} \right)}}}}$

Whatever the circumstances, the coefficients of a weighting matrix maybe determined beforehand, either arbitrarily or on the basis ofexperimental trials.

For example, it is possible to establish a linear regression coefficientbetween two components i and j of the vector {right arrow over (A_(p)⁰)}(r), by considering a plurality of radial positions (r) in the sampleplane, so as to obtain a statistically significant sample. Thecoefficient k_(ij) of weighting matrix may then be determined dependingon this linear regression coefficient α_(ij), optionally assigned a termtaking into account the dispersion around the linear regression model.In such a case, the diagonal of the weighting matrix may consist ofcoefficients k_(ii) equal to 1.

This allows a weighting function F_(i,p) ⁰, associated with thewavelength λ_(i), taking into account the correlation between thevarious terms of the vector {right arrow over (A_(p) ⁰)}(r) to beestablished.

Variants Regarding the Light Source or the Photodetector.

In the examples given with reference to FIGS. 1 and 2, the light source11, able to emit a light wave 12 in various spectral bands, includesthree elementary light sources 11 ₁, 11 ₂, 11 ₃, taking the form oflight-emitting diodes emitting in a first spectral band λ₁, a secondspectral band λ₂, and a third spectral band λ₃, respectively, thespectral bands being different from one another, and, preferably, notoverlapping.

The light source 11 may also include a white light source 11 _(w) placedupstream of a filtering device 19, for example a filter wheel, able toplace a filter of pass band λ_(i) between the white light source and thesample, as shown in FIG. 5, such that the image I_(i) formed by thephotodetector 16 is representative of said pass band λ_(i). A pluralityof filters, having pass bands that are different from one another, arethen successively placed between the light source 11 _(w) and the sample10.

According to one variant, the filtering device 19 may also be a tri-bandfilter, defining a plurality of spectral bands. An example of a filtersuitable for this application is the Edmund. Optics 458, 530 & 628 nmtri-band filter, which defines spectral bands centered on the wavelengthof 458 nm, 530 nm and 628 nm, respectively. This allows the sample to beilluminated simultaneously using 3 wavelengths.

The use of a diffuser 17, such as described above, between the lightsource and the diaphragm 18 is preferable, whatever the embodiment.

The photodetector 16 may, as described above, be an RGB matrix-arrayphotodetector, this allowing the various images I₁ . . . I_(i) . . .I_(N) to be acquired in the various spectral bands λ₁ . . . λ_(i) . . .λ_(N) in succession or simultaneously. In this case, the light sourcemay be a white light source 11 _(w), in which case the various imagesmay be acquired simultaneously.

It may also be a question of a monochromatic photodetector 16, in whichcase the light source 11 is able to generate, in succession, a lightwave in various spectral bands λ₁ . . . λ_(i) . . . λ_(N). In such aconfiguration, the light source includes either a plurality ofelementary light sources 11 ₁, 11 ₂, 11 ₃, or a filtering device 19, asdescribed above. In such a case, the sample is exposed in succession toincident light waves 12 ₁ . . . 12 _(i) . . . 12 _(N), N being thenumber of spectral bands in question. An image I_(i) (1≤i≤N),representative of the light wave 22 _(i) transmitted by the sample isthen acquired on each exposure.

Realized Trials.

Trials were carried out in the configuration shown in FIG. 1 anddescribed above. The sample was an anatomopathology slide, including across section of colon stained with hematoxylin eosin saffron. The lightsource was placed at a distance Δ equal to 5 cm from the sample, thisdistance separating the diaphragm 18 from the sample 10.

FIGS. 6A, 6B and 6C show an image of the modulus |A_(1,p) ⁰(r)| of thecomplex amplitude A_(1,p) ⁰(r) of the wave 22 ₁ transmitted by thesample, in the plane P₀ of the sample, in the first spectral band λ₁extending between 450 and 465 nm, these images being obtained after anumber of iterations p equal to 1, 3 and 10, respectively.

FIGS. 7A, 7B and 7C show an image of the modulus |A_(2,p) ⁰(r)| of thecomplex amplitude A_(2,p) ⁰(r) of the wave 222 transmitted by thesample, in the plane P₀ of the sample, in the third spectral band λ₂extending between 520 and 535 nm, these images being obtained after anumber of iterations p equal to 1, 3 and 10, respectively.

FIGS. 8A, 8B and 8C show an image of the modulus |A_(3,p) ⁰(r)| of thecomplex amplitude A_(3,p) ⁰(r) of the wave 22 ₃ transmitted by thesample, in the plane P₀ of the sample, in the third spectral band λ₃extending between 620 and 630 nm, these images being obtained after anumber of iterations p equal to 1, 3 and 10, respectively. It will benoted that the average grayscale level of these images is higher thanthe grayscale level of the images of FIGS. 6A, 6B, 6C, 7A, 7B and 7C.This is due to the red-violet color of the sample.

FIGS. 9A, 9B and 9C show the combination of the images 6A-7A-8A, 6B-7B-8B, and 6C-7C-8C, respectively. These figures allow a colorrepresentation of the sample to be obtained, by simultaneously takinginto account the three spectral bands λ₁, λ₂ and λ₃.

In each series of images, an increase in contrast as a function of thenumber of iterations may be seen. It may also be noted that images thespatial resolution of which is satisfactory are formed when the numberof iterations is lower than or equal to 10, this limiting thecalculation time to a few seconds.

The method is therefore suitable for the high-rate, large-fieldobservation of samples. It allows images to be obtained in one or morespectral bands, making it compatible with the staining methods commonlyused in the field(s) of anatomical pathology and/or cytopathology.

The invention claimed is:
 1. A method for observing a sample,comprising: i) illuminating the sample using a light source thatproduces a light wave that propagates along a propagation axis; ii)acquiring, using a photodetector, a plurality of images of the sample,the images being formed in a detection plane, the sample being placedbetween the light source and the photodetector, each image of theplurality being representative of a light wave, transmitted by thesample under effect of the illumination, called the transmitted lightwave, and each image of the plurality being acquired in a spectral bandthat is different from that of other images of the plurality; iii)determining, based on each image respectively acquired in each spectralband, an initial complex amplitude of the transmitted light wave, insaid each spectral band, in the detection plane; iv) selecting a sampleplane, in which the sample lies, and back-propagating each complexamplitude established in the detection plane, in said each spectralband, in order to determine a complex amplitude of the transmitted wave,in said each spectral band, in the sample plane; v) calculating in saideach spectral band, based on a plurality of complex amplitudesdetermined in step iv), a weighted sum of the complex amplitudes, or oflogarithm functions thereof, or of argument functions thereof, in thesample plane, and calculating a weighting function, the weightingfunction being calculated using the weighted sum; vi) propagating theweighting function to the detection plane so as to obtain, for at leastone spectral band, a weighting function in the detection plane; vii)updating at least one complex amplitude of the transmitted light wave,in a spectral band, in the detection plane, using the weighting functionobtained, in the spectral band, in step vi); and viii) repeating stepsiv) to vii) until a stop criterion is reached, wherein, in step vii), anargument function of the complex amplitude of the transmitted lightwave, in a spectral band, in the detection plane, is calculateddepending on an argument function of the weighting function determined,in the detection plane and in the spectral band, in step vi).
 2. Themethod of claim 1, wherein, in step iii), a modulus of the complexamplitude of the transmitted light wave in a spectral band is determinedby normalizing the intensity of the image acquired by the photodetector,in the spectral band, by a reference intensity measured by thephotodetector in the absence of sample.
 3. The of claim 1, wherein, instep iv), the complex amplitude in a sample plane, in a spectral a, isdetermined by applying a propagation operator to the complex amplitude,defined in the same spectral band, in the detection plane.
 4. The methodof claim 1, wherein, in step vi), the weighting function, in thedetection plane, is propagated by applying a propagation operator to theweighting function determined, in the sample plane, in step v).
 5. Themethod of claim 1, wherein, in step vii), a modulus of the complexamplitude of the transmitted light wave, in a spectral band, in thedetection plane, is calculated depending on a modulus of the initialcomplex amplitude, in the spectral band.
 6. The method of claim 1,wherein, in stet v), the weighting function is common to all thespectral bands.
 7. The method of claim 1, wherein step v) furthercomprises determining a plurality of weighting functions, each weightingfunction of said plurality of weighting functions being associated withone spectral band.
 8. The method of claim 1, further comprising,following step viii): ix) forming an image representative of a modulusor of an argument function of the complex amplitude of the wavetransmitted by the sample, in the sample plane or in the detectionplane, in at least one spectral band.
 9. A device for observing asample, comprising: a light source configured to illuminate the sample;a photodetector, the sample being disposed between the light source andthe photodetector, the photodetector being configured to form aplurality of images, in a detection plane, of the light wave transmittedby the sample under effect of illumination by the light source, eachimage being obtained in a spectral band that is different from that ofother images of the plurality; and a processor, configured to processthe plurality of images by executing instructions, programmed into amemory, which, when executed, implement the method of claim 1.